Unsteady MHD free convective heat transfer flow along a vertical porous flat plate with internal heat generation

Abstract

In this study, a similarity analysis is made for an unsteady two-dimensional MHD free convective and heat transfer flow of a viscous incompressible fluid along a vertical flat plate with internal heat generation/absorption. The governing time-dependent boundary-layer equations are reduced to non-linear ordinary differential equations by introducing a similarity transformation. The obtained similarity equation for both steady and unsteady cases have been compared with previously published work and excellent agreement is found. The resulting local similarity equations for the unsteady flow have been solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Numerical results for the dimensionless velocity and temperature profiles as well as the local skin-friction coefficient and local Nusselt number are displayed both by graphically and numerically for different values of the physical parameters entering into the problem.The significance of the physical parameters on the flow field is discussed in detail.The results shows that the velocity profile and the temperature profile is much pronounced with the increasing value of heat generation and unsteadiness parameter but the opposite effect can be found for suction parameter and Prandlt number. Also, the result shows that the values of skin-friction and wall heat transfer are strongly influenced by unstediness and heat generation parameter.